Tā yīběnzhèngjīng de jiěshì le bàntiān, dàjiā dōu biē zhù le xiào.
She explained at length with an utterly straight face, and everyone suppressed their laughter.
Tips
usage
一本正经 often carries a slightly comic or ironic flavor — it describes someone who is being overly formal or solemn, especially when the context does not call for it. It can also describe genuine seriousness.